Finite Group Databasebeta

← #30615215

Subgroups — #30615215

Order 15616.

1782 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2#21462268C211yesmaximal, characteristic, complemented
3#21461723C212yesmaximal, complemented
4#21461687C214yesmaximal, complemented
5#21461657C212yesmaximal
6#21461589C214yesmaximal, complemented
7C2×C4×D4×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840785—21no—
10#16840784—21no—
11#16840783—21no—
12#16840782—21no—
13D61⋊(C4⋊C8)C2212yescomplemented
14C2×#14519839C2218yes—
15D61⋊(C22⋊C8)C2212yes—
16#16840721C2212yescomplemented
17#16840708C2212yescomplemented
18#16840706—21no—
19#16840704—21no—
20#16840704C2212yes—
21C4×C4⋊#6923—21no—
22C4×C4⋊#6923C2212yescomplemented
23#16840635C2218yescomplemented
24C22×D4×D61C2211yescharacteristic
25C23×C4×D61—21no—
26C2×C4×D244C411yescharacteristic, complemented
27C2×D4×Dic61C411yescharacteristic, complemented
28C2×#14519739C411yescharacteristic, complemented
29C2×C4×C22⋊D61—21no—
30C2×#14519737—21no—
31C4×D4×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34C4×D4×D61—21no—
35C4×D4×D61C412yescomplemented
36C4×D4×D61C412yescomplemented
37C4×D4×D61C2212yes—
38C4×D4×D61C2212yes—
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic, complemented
43C2×D61⋊C8C2314yes—
44#14519856—44no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—22no—
47C2×C4⋊#6923C2314yes—
48C2×C22⋊#6923—22no—
49C2×C4×#6923—22no—
50#14519844—22no—
51C4⋊#92420—22no—
52#14519839—216no—
53#14519834—22no—
54C22⋊#92420—22no—
55#14519832—22no—
56#14519832—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59C24×D61—21no—
60C22×D244C2×C411yescharacteristic
61C22×C22⋊D61—21no—
62C2×D4×D61—28no—
63C2×D4×D61—21no—
64C2×D4×D61—21no—
65C2×D4×D61C2×C412yes—
66C2×D4×D61C2312yes—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—48no—
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C4×D244—21no—
80C4×D244—21no—
81C4×D244C2×C412yes—
82C4×D244C2×C412yes—
83D4×Dic61—21no—
84D4×Dic61—21no—
85D4×Dic61C2×C412yes—
86D4×Dic61C2×C412yes—
87#14519739—21no—
88#14519739—21no—
89#14519739C2×C412yes—
90#14519739C2×C412yes—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95#14519737—22no—
96#14519737—22no—
97#14519737—22no—
98#14519737—22no—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196—21no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61C2×C412yes—
104C4⋊C4×D61C2312yes—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61C2×C411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61C2311yescharacteristic
122C42×D61C2311yescharacteristic
123C22×D4×C61C2×C411yescharacteristic
124C23×C4×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61C2×C412yes—
128C4×D4×C61C2×C412yes—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C42×C61C2×C411yescharacteristic
132C24×C61—21no—
133C23×D61—28no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—44no—
138C23×D61—42no—
139C23×D61—42no—
140C23×D61C2×D411yescharacteristic
141C22×#6923—24no—
142C2×D4×C61—24no—
143C2×D4×C61—21no—
144C2×D4×C61C22×C412yes—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—44no—
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22⋊C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—28no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—44no—
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162D4×D61—28no—
163D4×D61—28no—
164D4×D61—24no—
165D4×D61—24no—
166D4×D61—24no—
167D4×D61#4118yes—
168C2×D244—21no—
169C2×D244—24no—
170C2×D244C22×C412yes—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—48no—
182C2×C4×D61—48no—
183C2×C4×D61—48no—
184C2×C4×D61—44no—
185C2×C4×D61—44no—
186C2×C4×D61—44no—
187C2×C4×D61—48no—
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22⋊C411yescharacteristic
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22×C411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×C4×D61C2×D411yescharacteristic
199C2×C4×D61C2411yescharacteristic
200C22⋊#6923—44no—
201C2×#92420—24no—
202C4⋊#6923—28no—
203C4⋊#6923—44no—
204C4⋊#6923—44no—
205C4×#6923—44no—
206D61⋊C8—28no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61C22×C412yes—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C42×C61C22⋊C411yescharacteristic
212C42×C61C22⋊C411yescharacteristic
213C42×C61C22×C411yescharacteristic
214C42×C61C22×C411yescharacteristic
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—22no—
220#11758198—22no—
221C4⋊Dic61—21no—
222C4⋊Dic61C22×C412yes—
223#11758196—22no—
224#11758196—22no—
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22×C411yescharacteristic
232C4×Dic61C22×C411yescharacteristic
233C4×Dic61C2×D411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237C23×C61—24no—
238C23×C61—22no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61C2×C22⋊C411yescharacteristic
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—24no—
245C22×D61—28no—
246C22×D61—22no—
247C22×D61—28no—
248C22×D61—44no—
249C22×D61—416no—
250C22×D61—416no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—44no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—44no—
257C22×D61C2×C22⋊C411yescharacteristic
258C22×D61AGL(1,ℤ/8)12yes—
259C22×D61#13712yes—
260C22×D61C22×D411yescharacteristic
261C2×#6923—44no—
262C2×#6923—44no—
263C2×#6923—44no—
264D4×C61—24no—
265D4×C61—22no—
266D4×C61#11714yescomplemented
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—44no—
272C2×C4×C61—42no—
273C2×C4×C61—44no—
274C2×C4×C61C2×C22⋊C411yescharacteristic
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C23×C411yescharacteristic
280C22⋊D61—28no—
281C22⋊D61—28no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—44no—
287C2×Dic61—42no—
288C2×Dic61—44no—
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C22×D411yescharacteristic
295D244—24no—
296D244—22no—
297D244#11714yescomplemented
298C4×D61—22no—
299C4×D61—21no—
300C4×D61—21no—
301C4×D61—22no—
302C4×D61—21no—
303C4×D61—21no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—44no—
311C4×D61—44no—
312C4×D61—44no—
313C4×D61—44no—
314C4×D61—44no—
315C4×D61—44no—
316C4×D61AGL(1,ℤ/8)14yes—
317C4×D61C2×#4114yes—
318#92420—44no—
319#20738—611nomaximal, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—24no—
323C22×C61—48no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61#41712yes—
327C22×C61C22×C22⋊C411yescharacteristic
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—24no—
331C2×D61—24no—
332C2×D61—24no—
333C2×D61—416no—
334C2×D61—48no—
335C2×D61—42no—
336C2×D61—42no—
337C2×D61—48no—
338C2×D61—48no—
339C2×D61#41712yes—
340C2×D61#52512yes—
341C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
342C2×D61C2×AGL(1,ℤ/8)12yes—
343C2×D61C2×#13711yescharacteristic
344#6923—84no—
345C4×C61—21no—
346C4×C61—21no—
347C4×C61—21no—
348C4×C61—21no—
349C4×C61—42no—
350C4×C61#41812yes—
351C4×C61C2×#11712yes—
352Dic61—21no—
353Dic61—21no—
354Dic61—21no—
355Dic61—21no—
356Dic61—42no—
357Dic61#41812yes—
358Dic61#52512yes—
359C22×C4×D4—611no—
360C2×#432—611no—
361#2285—611no—
362#1824—612no—
363#1802—614no—
364#1786—612no—
365#1762—614no—
366C2×C61—22no—
367C2×C61—44no—
368C2×C61#228011yescharacteristic
369C2×C61C2×#41811yescharacteristic
370C2×C61C2×#41711yescharacteristic
371D61—22no—
372D61—44no—
373D61#310912yes—
374D61#311012yes—
375C23×D4—611no—
376C24×C4—1221no—
377C2×C4×D4—611no—
378C2×C4×D4—612no—
379C2×C4×D4—612no—
380C2×C4×D4—612no—
381C2×C4×D4—612no—
382C2×C4×D4—611no—
383C2×C4×D4—611no—
384C2×C4×D4—1221no—
385C2×C4×D4—1221no—
386C2×C4×D4—1221no—
387C2×C4×D4—1221no—
388C2×C4×D4—1221no—
389C2×C4×D4—1221no—
390C2×C4×D4#692311yescharacteristic, complemented
391C2×#117—1221no—
392C22×C4⋊C4—611no—
393C22×C22⋊C4—1221no—
394C22×C42—611no—
395#432—1221no—
396#432—1221no—
397#432—1221no—
398#432—1221no—
399C2×C4⋊C8—612no—
400C2×#102—618no—
401C2×C22⋊C8—612no—
402C2×#97—612no—
403#384—612no—
404#382—1221no—
405#380—612no—
406#380—1221no—
407C4×C4⋊C4—612no—
408C4×C4⋊C4—1221no—
409#340—618no—
410C61#2073811yescharacteristic, complemented, Sylow
411C25—1221no—
412C22×D4—612no—
413C22×D4—612no—
414C22×D4—611no—
415C22×D4—1221no—
416C22×D4—1221no—
417C22×D4—1221no—
418C22×D4—1228no—
419C22×D4C2×#692311yescharacteristic
420C23×C4—21no—
421C23×C4—611no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—1221no—
425C23×C4—1222no—
426C23×C4—1222no—
427C23×C4—1222no—
428C23×C4—1222no—
429C23×C4—1221no—
430C23×C4—1221no—
431C23×C4—1221no—
432C23×C4—2448no—
433C22×C8—614no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—612no—
437C4×D4—612no—
438C4×D4—612no—
439C4×D4—612no—
440C4×D4—612no—
441C4×D4—612no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1221no—
447C4×D4—1221no—
448C4×D4—1222no—
449C4×D4—1222no—
450C4×D4—1222no—
451C4×D4—1222no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1221no—
455C4×D4—1221no—
456C4×D4C2×#692312yes—
457C4×D4C2×#692312yes—
458#117—2444no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—612no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4—614no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1222no—
467C2×C4⋊C4—1222no—
468C2×C4⋊C4C2×#692311yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1222no—
471C2×C22⋊C4—1222no—
472C2×C22⋊C4—1222no—
473C2×C22⋊C4—1222no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1222no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—1222no—
490C2×C42C2×#692311yescharacteristic
491C4⋊C8—1222no—
492C4⋊C8—1222no—
493#102—12216no—
494C22⋊C8—1222no—
495C22⋊C8—1222no—
496#97—1222no—
497#97—1222no—
498#95—1222no—
499#95—1222no—
500C24—21no—
501C24—611no—
502C24—1222no—
503C24—1222no—
504C24—1228no—
505C24—1221no—
506C24—2442no—
507C24—2442no—
508C24—2444no—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—618no—
512C2×D4—612no—
513C2×D4—1224no—
514C2×D4—1224no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1224no—
518C2×D4—1228no—
519C2×D4—1228no—
520C2×D4—1228no—
521C2×D4—1224no—
522C2×D4—1221no—
523C2×D4C22×#692312yes—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—44no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—1224no—
544C22×C4—1224no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1224no—
557C22×C4—2444no—
558C22×C4—2448no—
559C22×C4—2448no—
560C22×C4—2448no—
561C22×C4—2444no—
562C22×C4—2448no—
563C22×C4—2444no—
564C22×C4—2444no—
565C22×C4C22⋊#692311yescharacteristic
566C22×C4C22⋊#692311yescharacteristic
567C22×C4C22×#692311yescharacteristic
568C2×C8—1224no—
569C2×C8—1228no—
570C4⋊C4—21no—
571C4⋊C4—612no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1228no—
575C4⋊C4—1221no—
576C4⋊C4—2444no—
577C4⋊C4—2444no—
578C4⋊C4C22×#692312yes—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—1222no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—1222no—
587C22⋊C4—2444no—
588C42—611no—
589C42—611no—
590C42—611no—
591C42—611no—
592C42—611no—
593C42—611no—
594C42—611no—
595C42—611no—
596C42—611no—
597C42—611no—
598C42—611no—
599C42—611no—
600C42—2444no—
601C42C22⋊#692311yescharacteristic
602C42C22⋊#692311yescharacteristic
603C42C22×#692311yescharacteristic
604C42C22×#692311yescharacteristic
605C23—24no—
606C23—22no—
607C23—42no—
608C23—42no—
609C23—611no—
610C23—612no—
611C23—612no—
612C23—611no—
613C23—1222no—
614C23—1222no—
615C23—1228no—
616C23—1224no—
617C23—1228no—
618C23—1222no—
619C23—2442no—
620C23—2444no—
621C23—2442no—
622C23—2442no—
623C23—2444no—
624C23—2444no—
625C23—24416no—
626C23—24416no—
627C23—2442no—
628C23C2×C22⋊#692311yescharacteristic
629D4—24no—
630D4—22no—
631D4—614no—
632D4—1224no—
633D4—1228no—
634D4—1228no—
635D4—1222no—
636D4#1451985614yescomplemented
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—44no—
642C2×C4—42no—
643C2×C4—44no—
644C2×C4—611no—
645C2×C4—611no—
646C2×C4—614no—
647C2×C4—614no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—611no—
651C2×C4—611no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4—2444no—
672C2×C4—2444no—
673C2×C4—2444no—
674C2×C4—2444no—
675C2×C4—2444no—
676C2×C4—2444no—
677C2×C4—2444no—
678C2×C4—2442no—
679C2×C4—2444no—
680C2×C4C2×C22⋊#692311yescharacteristic
681C2×C4C2×C22⋊#692311yescharacteristic
682C2×C4C2×C22⋊#692311yescharacteristic
683C2×C4C2×C22⋊#692311yescharacteristic
684C2×C4C2×C22⋊#692311yescharacteristic
685C2×C4C23×#692311yescharacteristic
686C8—2444no—
687C22—21no—
688C22—21no—
689C22—24no—
690C22—48no—
691C22—42no—
692C22—42no—
693C22—612no—
694C22—611no—
695C22—611no—
696C22—612no—
697C22—612no—
698C22—1224no—
699C22—1224no—
700C22—1221no—
701C22—1221no—
702C22—1224no—
703C22—2448no—
704C22—2448no—
705C22—2448no—
706C22—24416no—
707C22—2442no—
708C22—2442no—
709C22#1684075312yes—
710C22C22×C22⋊#692311yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—42no—
716C4—612no—
717C4—612no—
718C4—1221no—
719C4—1221no—
720C4—1221no—
721C4—1221no—
722C4—4884no—
723C4—2442no—
724C4#1684075412yes—
725C4C2×#1451985612yes—
726C2—22no—
727C2—44no—
728C2—612no—
729C2—612no—
730C2—1222no—
731C2—2444no—
732C2#2146226311yescharacteristic
733C2C2×#1684075411yescharacteristic
734C2C2×#1684075311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#20738
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. #21462268C2semidirect
3. #21461723C2semidirect
4. #21461687C2semidirect
6. #21461589C2semidirect
13. D61⋊(C4⋊C8)C22semidirect
16. #16840721C22semidirect
17. #16840708C22semidirect
22. C4×C4⋊#6923C22semidirect
23. #16840635C22semidirect
26. C2×C4×D244C4semidirect
27. C2×D4×Dic61C4semidirect
28. C2×#14519739C4semidirect
35. C4×D4×D61C4semidirect
36. C4×D4×D61C4semidirect
42. C2×C4×D4×C61C4semidirect
266. D4×C61#117semidirect
297. D244#117semidirect
390. C2×C4×D4#6923semidirect
410. C61#20738semidirect
636. D4#14519856semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D61⋊#4322
#214622682
#214617232
#214616872
#214616572
#214615892
C2×C4×D4×D612
#2073861